The Federal Reserve Bank of New York is out with a new study of the labor market for college grads, and lurking within it is a factoid that I imagine will have a long and fruitful life bouncing around the Internet. It finds that just 27 percent of bachelor's degree holders work in jobs "directly related" to their college major, as shown in the graph below on the right.

Meanwhile, as shown on the left, they find just 62 percent of BA's have a job even requiring their degree, which implies a very, very large number of over-educated, underemployed Americans are wasting their talents in the workforce.

We'll get to both stats in time, but let's start with the bit about college majors. When I say the 27 percent figure is a "factoid," I mean it in Norman Mailer's original sense -- something that looks and smells sort of like a fact, but is not one. There a couple reasons why. First, the study doesn't look at Americans with graduate degrees, so any pre-med students who actually became doctors don't get counted, nor do econ grads who went on to get MBA's or English teachers who got went from comp lit to a master's in education. That might seem like a nitpick, until your realize that more than a third of BA's 25 or older have an advanced degree.

But there are other, more fundamental reasons why the figure is a bit suspect. To figure out which workers had jobs that were related to their major, the authors matched Census data against the National Center for Education Statistics's Occupational Crosswalks. As Matt Yglesias pointed out, the government appears to think his philosophy degree was only good for becoming a college professor, despite the fact that the analysis skills it imparted seem to have served him just fine as a journalist. For fun, I went and checked out what the government believes math majors are supposed to go and do with their lives. The options: professor, math scientist, mathematician, natural science managers, and statisticians. I don't know about you, but the math majors I knew in college went off and made money on Wall Street (or as consultants, if they were into travel). I'm sure their quantitative skills came in handy often enough.

The point here isn't just that the government has fouled up its database. Rather, it's that actually figuring out what any given field of study will prepare students for in an ever-evolving economy is probably an impossible task.

Now, about that other chart. Are 38 percent of B.A.'s really underemployed? The answer really depends on how you play with the data. I know that's not satisfying, but it's honest. We're beginning to accumulate a decently rich vein of literature that tries to get at this issue, and the conclusions tend to hinge on arcane methodological issues. I've seen numbers suggesting the the underemployment problem is worse. I've seen numbers suggesting the problem is probably better. But you need to look at each conclusion in the context of a larger body of research, as one more stroke on the canvas.

Now, in fairness, the stats I've focused on here aren't actually the heart of the NY Fed's study. Its main finding is that, according to their definitions, a college grad is slightly more likely to find an appropriate job in larger metro areas than smaller ones, because the labor market is bigger and denser. It's a neat, somewhat intuitive finding that seems to confirm the idea that major, tightly-packed cities are healthier building blocks for an economy than diffuse sprawl.

But like I said, these are the sorts of figures seem tailor-made to travel around Twitter. So for today, just remember: Whenever it comes to big, bold statistics about the fate of college grads, reader beware.